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Consider the function \( \mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}x^{2}-1, & -1 \leq x \leq 1 \\ \ell n x, & 1x \leq e\end{array}\right. \)
\( \mathrm{P} \)
Let \( \quad \mathrm{f}_{1}(\mathrm{x})=\mathrm{f}(|\mathrm{x}|) \)
\[
\begin{array}{l}
f_{2}(x)=|f(x)| \\
f_{3}(x)=f(-x)
\end{array}
\]
Now answer the following questions.
If \( f_{4}(x)=\log _{27}\left(f_{3}(x)+2\right) \), then range of \( f_{4}(x) \) is
(a) \( [1,9] \)
(b) \( \left[\frac{1}{3}, \infty\right) \)
(c) \( \left[0, \frac{1}{3}\right] \)
(d) \( [1,27] \)
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